Former deputy prime minister Lord Prescott said he had "finally got justice" after the Metropolitan Police force admitted it failed to warn victims and potential victims of phone hacking at the time of its original investigation into the scandal.

Lord Prescott's comment came after lawyers acting for him and for MP Chris Bryant, ex-Met Police deputy assistant commissioner Brian Paddick, actor Jude Law's personal assistant Ben Jackson and an anonymous individual known as HJK announced that the force accepted it had "breached a legal obligation" to warn victims.

Law firm Bindmans, representing the five, said the Met formally admitted "that its failure in 2006 and 2007 to warn victims and potential victims of phone-hacking was unlawful".

Two judges at the High Court heard that a judicial review action launched by Lord Prescott and the others against the Met in September 2010 had settled.

After the hearing in London, the Metropolitan Police Service (MPS) said it was "pleased to have reached an agreement" in the case and "accepts that more should have been done by police in relation to those identified as victims and potential victims of phone hacking several years ago".

Lord Prescott, who attended the proceedings, said: "It's taken me 19 months to finally get justice. Time and time again I was told by the Metropolitan Police that I had not been targeted by Rupert Murdoch's News of the World. But I refused to accept this was the case. Thanks to this judicial review, the Metropolitan Police has finally apologised for its failure to inform victims of the criminal acts committed by the News of the World against myself and hundreds of other victims of phone hacking."

Lord Justice Gross and Mr Justice Irwin were told that the claimants and the Met had agreed a "declaration" in which the Met admits it breached its duties under Article 8 of the European Convention on Human Rights, which provides that "everyone has the right to respect for his private and family life, his home and his correspondence".

The MPS said: "It is a matter of public record that the unprecedented increase in anti-terrorist investigations resulted in the parameters of the original inquiry being tightly drawn and officers considered the prosecution and conviction of Clive Goodman and Glenn Mulcaire as a successful outcome of their investigation.

"There are now more than 130 officers involved in the current phone-hacking inquiry (Weeting) and the two operations being run in conjunction with it, and this in part reflects the lessons that have been learned about how police should deal with the victims of such crimes. This settlement does not entail damages being paid by the MPS and, as the court has made clear, sets no precedent for the future.

"How the MPS treats victims goes to the very heart of what we do. It was important that this case did not result in such a wide duty being placed on police officers that it could direct them away from their core purpose of preventing and detecting crime. All the claimants are receiving personal apologies from the MPS."